A386272 Expansion of 1/(1 - 49*x)^(3/7).
1, 21, 735, 29155, 1224510, 53143734, 2356038874, 106021749330, 4823989594515, 221367522503855, 10227179539678101, 475098976797773601, 22171285583896101380, 1038639455430209672340, 48816054405219854599980, 2300863364299362480145724, 108715793963144877186885459
Offset: 0
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(1/(1-49*x)^(3/7))
Formula
a(n) = (-49)^n * binomial(-3/7,n).
a(n) = 7^n/n! * Product_{k=0..n-1} (7*k+3).
a(n) = 7^n * Product_{k=1..n} (7 - 4/k).
D-finite with recurrence n*a(n) +7*(-7*n+4)*a(n-1)=0. - R. J. Mathar, Jul 20 2025